The diameter of the moon is approximately one fourth of the diameter of the earth.Find the ratio of their surface areas.

The surface area of a sphere is given by the formula 4πr², where r is the radius of the sphere.

Step 1: Given that the diameter of the moon is one fourth of the diameter of the earth, the radius of the moon is also one fourth of the radius of the earth. Let's denote the radius of the earth as R. Then the radius of the moon is R/4.

Step 2: The surface area of the earth is 4πR² and the surface area of the moon is 4π(R/4)².

Step 3: To find the ratio of their surface areas, we divide the surface area of the moon by the surface area of the earth.

This gives us [4π(R/4)²] / [4πR²] = (R/4)² / R² = 1/16.

So, the ratio of the surface area of the moon to the surface area of the earth is 1:16.